(p,N)策略Geo/G/1排队的一个推广模型及其最优(p*,N*)策略分析OA

This article considers a discrete-time Geo/G/1 queue with different arrival rates,Bernoul-li feedback service,and(p,N)-startup policy.During server busy and idle periods,the customers arrive with different arrival rates.When a server busy period ends,the system will be shut down.If the Nth customer comes,the service will begin with probability p(0 ≤ p ≤ 1),or the service will not begin until the(N+1)th customer arrives with probability 1-p.The customer who is just served departs with probabilityθ(0 ≤ θ ≤ 1),or asks for a service again with probability 1-θ.Using total probability decomposition and limit theorem of z transform,the transit and steady-state results for queue length distribution probability are obtained,and an important index for departure process—expected departure number per unit time is analyzed.By defining system cost per unit time,the optimal policy(p*,N*)that minimizes system cost is theoretically studied.Numerically,the steady-state queue length probabilities and optimal policy(p*,N*)are demonstrated,which offers managers theoretical reference for economical decision.